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Diskretnaya Matematika, 2018, Volume 30, Issue 4, Pages 42–47
DOI: https://doi.org/10.4213/dm1533 (Mi dm1533) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Centrally essential rings which are not necessarily unital or associative

V. T. Markova, A. A. Tuganbaevba

a Lomonosov Moscow State University
b National Research University "Moscow Power Engineering Institute"
Full-text PDF (136 kB) Citations (6)
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DOI: https://doi.org/10.4213/dm1533
Abstract: Centrally essential rings were defined earlier for associative unital rings; in this paper, we define them for rings which are not necessarily associative or unital. In this case, it is proved that centrally essential semiprime rings are commutative. It is proved that all idempotents of a centrally essential alternative ring are central. Several examples of non-commutative centrally essential rings are provided, some properties of centrally essential rings are described.
Keywords: centrally essential ring, semiprime ring, idempotent, non-unital ring, alternative ring.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00895-A
Russian Science Foundation 16-11-10013
Received: 26.07.2018
English version:
Discrete Mathematics and Applications, 2019, Volume 29, Issue 4, Pages 215–218
DOI: https://doi.org/10.1515/dma-2019-0019
Bibliographic databases:
Document Type: Article
UDC: 512.55
Language: Russian
Citation: V. T. Markov, A. A. Tuganbaev, “Centrally essential rings which are not necessarily unital or associative”, Diskr. Mat., 30:4 (2018), 42–47; Discrete Math. Appl., 29:4 (2019), 215–218
Citation in format AMSBIB
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\pages 42--47
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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